Factor 2x^2-7x-15

Problem

2*x2−7*x−15

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=2 b=−7 and c=−15

2. Calculate the product of a and c which is 2×−15=−30

3. Find two numbers that multiply to −30 and add to the middle coefficient b=−7 These numbers are −10 and 3

4. Rewrite the middle term −7*x using the two numbers found: 2*x2−10*x+3*x−15

5. Factor by grouping the first two terms and the last two terms: 2*x*(x−5)+3*(x−5)

6. Factor out the common binomial factor (x−5)

Final Answer

2*x2−7*x−15=(2*x+3)*(x−5)

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